Valuation of options

Further information: Option: Model implementation

In finance, a price (premium) is paid or received for purchasing or selling options. This price can be split into two components.

These are:

• Intrinsic Value
• Time Value

Contents 1 Intrinsic Value 2 Time Value 3 Pricing models 4 References

Intrinsic Value

If the market value is more than the strike price, then a call option is 'In the Money'. The difference between the two is called the Intrinsic Value.

In simple words, it is the value by which is already available in the market. If you are holding NIFTY 5000 Call (Bullish/Long) option and NIFTY is at 5050 level then you already have 50 Rs advantage even if the option expires today. These 50 Rs is the intrinsic value of option.

Conversely if you are holding a put option and NIFTY is below strike price then your option has an intrinsic value equalling the difference between the strike price and NIFTY value. So,

Intrinsic Value

= Current Stock Price – Strike Price (Call Option)

= Strike Price – Current Stock Price (Put Option)

Time Value

The option premium is always greater than intrinsic value. This extra money is for the risk which the option writer/seller is undertaking. This is called the Time Value.

Time value is the amount the option trader is paying for a contract above its intrinsic value, with the belief that prior to expiration the contract value will increase because of a favourable change in the price of the underlying asset. Obviously, the longer the amount of time until the expiry of the contract, the greater the time value. So,

Time Value = Option Premium – Intrinsic Value

There are many factors which determine Option Premium. These factors affect the premium of the option with varying intensity. Some of these factors are listed here:

• Price of the underlying: Any fluctuation in the price of the underlying (stock/index/commodity) obviously has the largest impact on premium of an option contract. An increase in the underlying price increases the premium of call option and decreases the premium of put option. Reverse is true when underlying price decreases.
• Strike price: How far is the strike price from spot also has an impact on option premium. Say, if NIFTY goes from 5000 to 5100 the premium of 5000/5100 strike will change a lot compared to a contract with strike of 5500 or 4700.
• Time till expiry: Lesser the time to expiry, option premium follows the intrinsic value more closely. On the expiry date Time Value approached zero.
• Volatility of underlying: Underlying security is a constantly changing entity. The degree by which its price fluctuates can be termed as volatility. So a share which fluctuates 5% on either side on daily basis is said to have more volatility than let’s say a stable blue chip shares whose fluctuation is more benign at 2-3%. Volatility affects calls and puts alike. Higher volatility increases the option premium because of greater risk it brings to the seller.

Apart from above, other factors like bond yield (or interest rate) also affect the premium. This is due to the fact that the money invested by the seller can earn this risk free income in any case and hence while selling option; he has to earn more than this because of higher risk he is taking.

Sometimes dividend payment by an underlying is also factored in to the premium as it affects the cost of buying those shares directly rather than buying the option.^[1]

Pricing models

Because the values of option contracts depend on a number of different variables in addition to the value of the underlying asset, they are complex to value. There are many pricing models in use, although all essentially incorporate the concepts of rational pricing, Moneyness, Option time value and Put-call parity.

Amongst the most common models are:

• Black–Scholes and the Black model
• Binomial options pricing model
• Monte Carlo option model
• Finite difference methods for option pricing

Other approaches include:

• Heston model
• Heath-Jarrow-Morton framework
• Variance Gamma Model (see variance gamma process)

References

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